
If the acceleration due to gravity is g , a sphere of lead of density is gently released in a column of liquid of density d , the sphere will fall vertically with:
(A) An acceleration of 8
(B) No acceleration
(C) An acceleration of
(D) An acceleration
Answer
140.1k+ views
Hint There are two forces acting on the sphere. So, the net force on the sphere is calculated by taking the difference between the gravitational and buoyancy force. Then by using the relation the acceleration can be evaluated.
Complete step-by-step solution
When the sphere is falling through the column let its volume be V. Since, density is the ratio of mass to volume, mass of the sphere can be written as
When it is released in the liquid, the volume remains the same and the density is d. So, m inside the liquid can be written as .
During its motion down the column,
Gravitational force acting downwards is given by,
Buoyancy force acting upwards is given by,
The net force acting is
Since acceleration is
Hence the acceleration during its fall is
The correct option is C.
Note According to Archimedes principle, when a body is immersed partially or wholly in a fluid, at rest, it is buoyed up with force equal to the weight of the fluid displaced by the body.
Also, the ratio of weight of the object immersed to weight of displaced fluid is equal to the ratio of the density of the object to that of fluid (d)
Complete step-by-step solution
When the sphere is falling through the column let its volume be V. Since, density is the ratio of mass to volume, mass of the sphere can be written as
When it is released in the liquid, the volume remains the same and the density is d. So, m inside the liquid can be written as
During its motion down the column,
Gravitational force acting downwards is given by,
Buoyancy force acting upwards is given by,
The net force acting is
Since acceleration is
Hence the acceleration during its fall is
The correct option is C.
Note According to Archimedes principle, when a body is immersed partially or wholly in a fluid, at rest, it is buoyed up with force equal to the weight of the fluid displaced
Also, the ratio of weight of the object immersed
Latest Vedantu courses for you
Grade 8 | CBSE | SCHOOL | English
Vedantu 8 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹42,500 per year
EMI starts from ₹3,541.67 per month
Recently Updated Pages
JEE Main Participating Colleges 2024 - A Complete List of Top Colleges

JEE Main Maths Paper Pattern 2025 – Marking, Sections & Tips

Sign up for JEE Main 2025 Live Classes - Vedantu

JEE Main 2025 Helpline Numbers - Center Contact, Phone Number, Address

JEE Main Course 2025 - Important Updates and Details

JEE Main 2025 Session 2 Form Correction (Closed) – What Can Be Edited

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

JEE Main Exam Marking Scheme: Detailed Breakdown of Marks and Negative Marking

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

Other Pages
Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line
